Incident logging is critical for IT Service Management for the following reasons:
The first and perhaps most obvious reasons is you want to know if there are pending incidents that need to be resolved. When supporting a service, you want to make sure that everything is working as it should. You would not want to miss resolving an incident that would affect say a major service used by your company.
There are many kinds of incidents. A PC used by a customer service representative may not be as critical as say, a central computer crashing. In the first case, the effect is probably only to one person while the second case affects practically the entire company.These incidents can be called critical incidents, severity 1 incidents, high priority incidents or whatever.